Rolling diaphragm assemblies are known to have been used in flow control metering valves in automotive applications, e.g. internal combustion engines, while printing applications that utilize diaphragms conventionally have used disk-shaped diaphragms and valves to pump small quantities of ink from reservoirs to printers via flexible tubes and conduits. Recent advances in ink-jet printhead priming and flushing are described in my co-pending U.S. patent application Ser. No. 07/949,318, filed Sep. 21, 1992 entitled "Automatic Failure Recovery Method and System for Ink-jet Printheads", which is subject to common ownership herewith. The system described therein requires a vacuum-and-flush tube, a rotating cam, and a tube pinch-off follower member per printhead, as well as a common diaphragm-type pump, drive motor clutch mechanism and firmware for synchronously controlling a drive motor's forward and reverse rotation. The system is effective in priming and flushing ink from plural printheads, thus to avoid clogging of the printheads' nozzles, but it involves many moving parts and their attendant cost of production and maintenance and it is subject to accumulation of ink and particulate in the tubes. The system also requires a relatively long, e.g. twenty second or more, cycle time during which the ink-jet printer is out of service.